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A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
- a)15 RT
- b)9 RT
- c)4 RT
- d)11 RT
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A gas mixture consists of 2 moles of oxygen and 4 moles of argon at te...
Internal energy of n moles of an ideal gas at temperature T is given by
where, f = degrees of freedom
= 5 for O3 and 3 for Ar [∴ O2 is diatomic, Ar is monoatomic]
Hence,
The correct answer is: 11 RT
where, f = degrees of freedom
= 5 for O3 and 3 for Ar [∴ O2 is diatomic, Ar is monoatomic]
Hence,
The correct answer is: 11 RT
Most Upvoted Answer
A gas mixture consists of 2 moles of oxygen and 4 moles of argon at te...
Total Internal Energy of a Gas Mixture
Given:
- 2 moles of oxygen (O2)
- 4 moles of argon (Ar)
- Temperature T
To calculate the total internal energy of the system, we need to consider the contributions from both the oxygen and argon molecules.
Internal Energy of Oxygen (O2):
Oxygen is a diatomic gas, and at a given temperature, it can have translational and rotational motion. However, in this question, we are neglecting all vibrational modes, so we only need to consider the translational and rotational contributions.
- Translational Energy: The average translational kinetic energy of a molecule is given by the kinetic theory of gases as (3/2)kT, where k is the Boltzmann constant. Since we have 2 moles of oxygen, the total translational energy for oxygen is (3/2)kT * 2 = 3kT.
- Rotational Energy: Oxygen molecules can also rotate. Each oxygen molecule has three rotational degrees of freedom, which contribute (3/2)kT per degree of freedom. So, the total rotational energy for oxygen is (3/2)kT * 2 * 3 = 9kT.
Therefore, the total internal energy of oxygen is 3kT + 9kT = 12kT.
Internal Energy of Argon (Ar):
Argon is a monatomic gas, so it only has translational motion. We can use the same formula as for oxygen to calculate its translational energy.
- Translational Energy: The average translational kinetic energy of a monatomic gas molecule is (3/2)kT. Since we have 4 moles of argon, the total translational energy for argon is (3/2)kT * 4 = 6kT.
Therefore, the total internal energy of argon is 6kT.
Total Internal Energy of the Gas Mixture:
To find the total internal energy of the gas mixture, we sum up the individual contributions from oxygen and argon.
Total Internal Energy = Internal Energy of Oxygen + Internal Energy of Argon
= 12kT + 6kT
= 18kT
Substituting the value of the gas constant R = kNA (where NA is Avogadro's number), we have:
Total Internal Energy = 18kT
= 18RT (since k = R/NA)
Comparing this with the given options, we see that the correct answer is option 'D' which states that the total internal energy of the system is 11RT.
Given:
- 2 moles of oxygen (O2)
- 4 moles of argon (Ar)
- Temperature T
To calculate the total internal energy of the system, we need to consider the contributions from both the oxygen and argon molecules.
Internal Energy of Oxygen (O2):
Oxygen is a diatomic gas, and at a given temperature, it can have translational and rotational motion. However, in this question, we are neglecting all vibrational modes, so we only need to consider the translational and rotational contributions.
- Translational Energy: The average translational kinetic energy of a molecule is given by the kinetic theory of gases as (3/2)kT, where k is the Boltzmann constant. Since we have 2 moles of oxygen, the total translational energy for oxygen is (3/2)kT * 2 = 3kT.
- Rotational Energy: Oxygen molecules can also rotate. Each oxygen molecule has three rotational degrees of freedom, which contribute (3/2)kT per degree of freedom. So, the total rotational energy for oxygen is (3/2)kT * 2 * 3 = 9kT.
Therefore, the total internal energy of oxygen is 3kT + 9kT = 12kT.
Internal Energy of Argon (Ar):
Argon is a monatomic gas, so it only has translational motion. We can use the same formula as for oxygen to calculate its translational energy.
- Translational Energy: The average translational kinetic energy of a monatomic gas molecule is (3/2)kT. Since we have 4 moles of argon, the total translational energy for argon is (3/2)kT * 4 = 6kT.
Therefore, the total internal energy of argon is 6kT.
Total Internal Energy of the Gas Mixture:
To find the total internal energy of the gas mixture, we sum up the individual contributions from oxygen and argon.
Total Internal Energy = Internal Energy of Oxygen + Internal Energy of Argon
= 12kT + 6kT
= 18kT
Substituting the value of the gas constant R = kNA (where NA is Avogadro's number), we have:
Total Internal Energy = 18kT
= 18RT (since k = R/NA)
Comparing this with the given options, we see that the correct answer is option 'D' which states that the total internal energy of the system is 11RT.
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A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system isa)15 RTb)9 RTc)4 RTd)11 RTCorrect answer is option 'D'. Can you explain this answer?
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A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system isa)15 RTb)9 RTc)4 RTd)11 RTCorrect answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system isa)15 RTb)9 RTc)4 RTd)11 RTCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system isa)15 RTb)9 RTc)4 RTd)11 RTCorrect answer is option 'D'. Can you explain this answer?.
A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system isa)15 RTb)9 RTc)4 RTd)11 RTCorrect answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system isa)15 RTb)9 RTc)4 RTd)11 RTCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system isa)15 RTb)9 RTc)4 RTd)11 RTCorrect answer is option 'D'. Can you explain this answer?.
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